Logging devices that measure formation electromagnetic properties (e.g. dielectric constant) are known, for example from U.S. Pat. No. 3,849,721, U.S. Pat. No. 3,944,910 and U.S. Pat. No. 5,434,507. FIG. 2 illustrates a logging device including a transmitter T and spaced receivers R1, R2 mounted in a pad P that is urged against a borehole wall WBW of a well bore WB filled with drilling mud DM. Microwave electromagnetic energy (illustrated by dotted lines) is transmitted into the formations, and energy that has propagated through the formations is received at the receiving antennas. The phase and amplitude of the energy propagating in the formation is determined from the receiver output signals. The dielectric constant and the conductivity of the formations can then be obtained from the phase and amplitude measurements.
The transmitters and receivers comprise antennas that are assimilated to magnetic dipoles. These dipoles are tangential to the pad face and are orientated in different directions. A broadside mode corresponds to the dipoles oriented orthogonally to the pad-axis. An endfire mode corresponds to the dipoles oriented in alignment with the pad axis. The depth of investigation for the broadside mode is very poor. The investigation depth for the endfire mode is greater than for the broadside mode, but the signal is usually weaker, for example at 1 GHz. The attenuation and phase-shift are measured between the two receivers. A simple inversion allows in case of a homogeneous formation to retrieve the dielectric constant and the conductivity. Typically, such a logging device is unable to provide an accurate measurement of the formation properties because of its high sensitivity to the standoff of the pad relatively to the formation or the presence of a mudcake on the borehole wall. For example, in the presence of a mudcake layer MC the number of unknowns increase from two unknown, namely the permittivity ∈ and the conductivity σ of the formation GF (∈, σ)gf to five unknowns, namely the permittivity ∈ and the conductivity σ of the formation (∈, σ)gf and of the mudcake MC (∈, σ)mc, and the mudcake thickness tmc. Consequently, accurate determination of the formation electromagnetic properties based on the attenuation and phase-shift measurements is not possible.
The document U.S. Pat. No. 5,345,179 proposes a solution to improve the logging device response and accuracy in the presence of a mudcake. The logging device comprises a plurality of cross-dipole antennas, each being located in a cavity. The cross-dipole antenna houses both endfire and broadside polarizations in the same cavity.
FIGS. 3 and 4 are perspective and cross-section views schematically showing a cross dipole antenna according to the prior art. Typically, such a cross dipole antenna 103 comprises two wires 132, 142 embedded in a non-resonant cavity 133 filled with a dielectric material and short-circuited to the conductive cavity wall at one end.
FIG. 5 illustrates the current distribution for a cross dipole antenna according to the prior art. The current distribution J is approximated from the analogy with a short-circuited transmission line. The current distribution on the radiating wire in the cavity can be approximated to:J(γ)=J0 cos(k0[γ−a])where:                J0 is the current amplitude,        a is the aperture size,        k0 is the wave number in the cavity and is equal to:        
            k      0        =                  ω        c            ⁢                        ɛ          cavity                      ,                ∈cavity is the relative dielectric constant of the material filling the cavity,        ω is the angular frequency, and        c is the speed of light in vacuum.        
The current is maximal at the short-circuit location. This cosinusoidal and asymmetric current distribution excites a strong, parasitic electric dipole.
FIGS. 6 and 7 illustrate the electromagnetic field components Ey and Ez in the yz plane of a cross dipole antenna 103 (more precisely of the radiating wire) of the prior art, respectively.
The current flowing on the wire, for example wire 132, excites modes in the cavity. The dominant mode is the transverse electric mode TE10. This mode contributes to a radiation pattern, which is close to a magnetic point dipole m orthogonal to the wire. The current distribution on the wire will also excite parasitic modes, the dominant one being the transverse magnetic mode TM11. This mode corresponds to an electric dipole p normal to the aperture. These parasitic modes cause a strong asymmetry of the electromagnetic field Ey and Ez in the yz plane.
The antennas of the prior art are far from being pure magnetic dipoles. In particular, the parasitic electric dipole, normal to the aperture affects the measurement accuracy. Further, as the mudcake electromagnetic properties are not determined, the inversion calculation for determining the geological formation electromagnetic properties may not be robust.